Axial flow around an array of cylinders is commonly encountered in nuclear reactors and heat exchangers. This geometry is subject to important flow instabilities. The chaotic flow fluctuations due to turbulence are not the only source of vortex structures: large-scale vortices have also been observed, both experimentally and numerically. The periodic pressure fluctuations caused by the coherent vortex structures are possibly a source of fretting and fatigue in the aforementioned applications. In order to comprehend this phenomenon, LargeEddy Simulations are performed on a numerical domain containing a single rigid cylinder with periodic boundary conditions, representative for a cylinder in an infinite square array. The research in this paper mainly focuses on the influence of the cylinder spacing, which is analyzed by calculating the Cross Spectral Density (CSD) function of the cylinder wall pressure for different cylinder spacings. The spectral analysis shows that the amplitude of the pressure fluctuations increases up to a well-determined intercylinder gap, after which it decreases exponentially for incrementing gap size. With the weakening of the instability, the location on the cylinder circumference where the maximum pressure amplitude occurs, changes as well. Finally, it is shown that the coherent vortices are transported as a whole at a convection speed which is dependent on the cylinder spacing. An updated model for this convection speed is proposed.